Problem: Simplify the following expression: $ p = \dfrac{8n}{9n + 2} + \dfrac{8}{3} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{8n}{9n + 2} \times \dfrac{3}{3} = \dfrac{24n}{27n + 6} $ Multiply the second expression by $\dfrac{9n + 2}{9n + 2}$ $ \dfrac{8}{3} \times \dfrac{9n + 2}{9n + 2} = \dfrac{72n + 16}{27n + 6} $ Therefore $ p = \dfrac{24n}{27n + 6} + \dfrac{72n + 16}{27n + 6} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{24n + 72n + 16}{27n + 6} $ $p = \dfrac{96n + 16}{27n + 6}$